You'll need to clarify what "loop cycle of my host" means. When Mobius syncs with a host, it has always offered two options for starting and stopping the initial recording: Beat and Bar. Beats are defined by the host tempo and bars are defined by the host time signature. You ask for that with two parameters, Sync Source will be set to Host and Sync Unit will be set to either Beat or Bar. Mobius 2.x did it the same way, though the names were different (SyncMode and Slave Sync Unit I believe).
If you are using a host that allows you to loop a multi-measure section of a host track, Mobius will not recognize the "loop point" of that track as something special, to Mobius it's just a Bar. For example, say you have a host track that is 32 bars long, you highlight bars 4 through 7 of that track and set the host to loop over that 4 bar section. When you press Record in Mobius, assuming you have SyncUnit=Bar, it waits for the next bar, which may be either 4, 5, 6, or 7. You can't tell it to wait for bar 4 and ONLY bar 4. Even though the host is looping, there is nothing in the VST specification that says "I'm at a loop point", Mobius only sees bars go by. Mobius 2.x worked the same way.
Most hosts are "linear hosts" that operate like a tape deck, recording starts and goes on forever, bar after bar. FL Studio is what I call a "looping host" in that it is itself a form of looper. Detecting when you are at the FL Studio loop point is challenging because VST doesn't give you that exact information and every host does loops in a slightly different way. I can try to do something that works in FL Studio, but then it may not work with Ableton, or Logic, or whatever. When you were using Mobius 2.x, were you using FL Studio as a host, or did you just recently switch to FL Studio?
There are a few ways around this. What most people do, is just adjust the timing of the Record Stop so that you press the button within the last bar of the host loop. If your host loops always have a fixed number of bars, say 4, you can use AutoRecord to record exactly 4 bars that match the host loop. You still have to start the recording on the right bar, because Mobius doesn't know which bar number means "start of the host loop".
Once you get that first loop recorded and of the right size, then we have more options for when the other functions happen, but let's focus on that initial recording first.